An alternate executive summary: "You sweat, you die."
(Quote courtesy Mr. L. Stroud, Esq.)

A few general thoughts:

The first problem in a situation like this is changing gears, mentally. You have now left one planet, rather suddenly, and arrived on another. The rules are radically different, and so is the definition of success. Understand and accept that the game has changed, radically; and adjust your actions and expectations to match. It takes practice and experience to switch gears like that. Momentum is tricky, it can put you on the wrong track.

I have found, on some of these situations, I try to think about what an experienced person that I know and trust would do. Talk it out; sometimes out loud; if it seems weird, who cares?. It is a conversation, kind of, and believe it or not it works. What would someone you respect, someone smarter than you, do? Where would their first priorities be?

The other consideration is acclimatization: this is huge. In my part of the world, we go from +35C to -45C annually. Given a chance, even a few days, the body adapts and adjusts remarkably. To go from one extreme to the other is potentially deadly. It is not about willpower; we are talking about physiological changes that are, I believe, measurable.

Last thought:
I have often heard that a first test for the risk of hypothermia is that you can't touch your thumb to your palm. I have been "fat fingered" many a time, and I think this has merit. It's a first indication that your core is shutting down heat/circulation to your extremities. It is a simple test, and a call to action. Opinions?